Once upon a time, I can remember saying I would never have any metric tools. Then came the replacement wheel cylinders which had metric bleeders. Then came this neighbor and that neighbor asking for help working on their junker which turned out requiring metric tools. Out of frustration finally, I broke down and bought a set of metric wrenches and sockets both up to 15mm sizes.
I keep the metric wrenches in a separate box from my SAE wrenches.
I keep the metric sockets in a separate box from my SAE sockets.
Since the boxes are identical for both, I have them both labelled.
Everything in my garage can be found in an instant due to meticulous organization.
I have used one of those partially open ended wrenches like your photo shows on the brake bleeder screws, but mine were not frozen up and I had at one time 3/8" bleeder screws (original). The wrench was 3/8" on one end, 7/16" on the other end.
I would not use that if the screw is locked tight. Go with a 6-point socket.
I have 1/2" drive, 3/8" drive and 1/4" drive sockets and wrench sets, each in separate boxes and labelled. Anytime I have ever needed to bleed brakes, I run straight for the 1/4" drive socket box.
Keep this up and eventually you will learn every nut and bolt size and length and threads per inch used on the car and where they are used.